Optimization Formulations and Static Equilibrium in Congested Transportations Networks.

In this paper we study the concepts of equilibrium and optimum in static transportation networks with elastic and non-elastic demands. The main mathematical tool of our paper is the theory of variational inequalities. We demonstrate that this theory is useful for proving the existence theorems. It can also justify Beckmann's formulation of the equilibrium problem. The main contribution of this paper is to propose a new definition of equilibrium, the normal equilibrium, which exists under very general assumptions.